# [R] how to estimate treatment-interaction contrasts

szhan at uoguelph.ca szhan at uoguelph.ca
Fri Jul 13 21:52:21 CEST 2007

```Hello, Chuck,
Thank you very much for your help! But the contrasts I want to do
simutaneously is
contrasts(B)
[,1] [,2] [,3] [,4]
b1   -4   -3   -2   -1
b2    1   -3   -2   -1
b3    1    2   -2   -1
b4    1    2    3   -1
b5    1    2    3    4

Could you please show me how to calculate estimates for ALL
intearaction constrasts using THESE contrasts? Say C2: c(-3, -3, 2, 2,
2) as an example. I used the ortholognal constrasts as you suggest,
estimate for interaction contrast C2 is still -24.1.
Joshua

Quoting Chuck Cleland <ccleland at optonline.net>:

> szhan at uoguelph.ca wrote:
>> Hello, R experts,
>> Sorry for asking this question again again since I really want a help!
>>
>> I have a two-factor experiment data and like to calculate estimates of
>> interation contrasts say factor A has levels of a1, a2, and B has
>> levels of b1, b2, b3, b4, and b5 with 3 replicates. I am not sure the
>> constrast estimate I got is right using the script below:
>>
>> score<-c(7.2,6.5,6.9,6.4,6.9,6.1,6.9,5.3,7.2,5.7,5.1,5.9,7.6,6.9,6.8,
>> 7.2,6.6,6.9,6.4,6.0,6.0,6.9,6.9,6.4,7.5,7.7,7.0,8.6,8.8,8.3)
>>
>> A <- gl(2, 15, labels=c("a1", "a2"))
>> B <- rep(gl(5, 3, labels=c("b1", "b2", "b3", "b4", "b5")), 2)
>>
>> contrasts(B)<-cbind(c(-4,rep(1,4)),c(rep(-3,2),rep(2,3)),
>> +  c(rep(-2,3),rep(3,2)),c(rep(-1,4), rep(4,1)))
>> fit1 <- aov(score ~ A*B)
>> summary(fit1, split=list(B=1:4), expand.split = TRUE)
>>                Df Sum Sq Mean Sq F value    Pr(>F)
>> A            1 3.2013  3.2013 15.1483 0.0009054 ***
>> B            4 8.7780  2.1945 10.3841 0.0001019 ***
>>      B: C1      1 0.0301  0.0301  0.1424 0.7099296
>>      B: C2      1 2.0335  2.0335  9.6221 0.0056199 **
>>      B: C3      1 1.2469  1.2469  5.9004 0.0246876 *
>>      B: C4      1 5.4675  5.4675 25.8715 5.637e-05 ***
>> A:B          4 5.3420  1.3355  6.3194 0.0018616 **
>>      A:B: C1    1 0.7207  0.7207  3.4105 0.0796342 .
>>      A:B: C2    1 2.6068  2.6068 12.3350 0.0021927 **
>>      A:B: C3    1 1.9136  1.9136  9.0549 0.0069317 **
>>      A:B: C4    1 0.1008  0.1008  0.4771 0.4976647
>> Residuals   20 4.2267  0.2113
>> ---
>> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>>
>> Now I like to get interaction contrast estimate for b1 and b2 vs
>> b3, b4 and b5
>> cont <- c(1, -1)[A] * c(-3, -3, 2, 2, 2)[B]
>>
>> estimat<-sum(cont*score) # value of the contrast estimate for A:B C2
>>
>>> estimat
>> [1] -24.1
>>
>> I am not sure the estimate for A:B C2 contrast  (-24.1) is correct
>> because the F value given the output above(12.3350) does not equal to
>> those I calculate below (15.2684):
>>
>> t.stat <- sum(cont*score)/se.contrast(fit1, as.matrix(cont))
>>> t.stat^2
>> Contrast 1
>>      15.2684
>>
>> interaction contrast and corresponding F value?
>> Joshua
>
>   If the contrasts for B are orthogonal, then you get the result you
> expected:
>
> score <- c(7.2,6.5,6.9,6.4,6.9,6.1,6.9,5.3,7.2,5.7,5.1,5.9,7.6,6.9,6.8,
>            7.2,6.6,6.9,6.4,6.0,6.0,6.9,6.9,6.4,7.5,7.7,7.0,8.6,8.8,8.3)
>
> A <- gl(2, 15, labels=c("a1", "a2"))
> B <- rep(gl(5, 3, labels=c("b1", "b2", "b3", "b4", "b5")), 2)
>
> contrasts(B) <- matrix(c(3, -1,  0,  0,
>                          3,  1,  0,  0,
>                         -2,  0,  2,  0,
>                         -2,  0, -1,  1,
>                         -2,  0, -1, -1), ncol=4, byrow=TRUE)
>
> fit1 <- aov(score ~ A*B)
>
> summary(fit1, split=list(B=1:4), expand.split = TRUE)
>
>             Df Sum Sq Mean Sq F value    Pr(>F)
> A            1 3.2013  3.2013 15.1483 0.0009054 ***
> B            4 8.7780  2.1945 10.3841 0.0001019 ***
>   B: C1      1 1.0427  1.0427  4.9340 0.0380408 *
>   B: C2      1 1.0208  1.0208  4.8304 0.0399049 *
>   B: C3      1 1.2469  1.2469  5.9004 0.0246876 *
>   B: C4      1 5.4675  5.4675 25.8715 5.637e-05 ***
> A:B          4 5.3420  1.3355  6.3194 0.0018616 **
>   A:B: C1    1 3.2267  3.2267 15.2684 0.0008734 ***
>   A:B: C2    1 0.1008  0.1008  0.4771 0.4976647
>   A:B: C3    1 1.9136  1.9136  9.0549 0.0069317 **
>   A:B: C4    1 0.1008  0.1008  0.4771 0.4976647
> Residuals   20 4.2267  0.2113
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>   Note that I put the contrast of interest for B in the first column of
> the contrast matrix.
>
> hope this helps,
>
> Chuck
>
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> and provide commented, minimal, self-contained, reproducible code.
>
> --
> Chuck Cleland, Ph.D.
> NDRI, Inc.
> 71 West 23rd Street, 8th floor
> New York, NY 10010
> tel: (212) 845-4495 (Tu, Th)
> tel: (732) 512-0171 (M, W, F)
> fax: (917) 438-0894
>

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